Upper Edge Detour Monophonic Number of a Graph

For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x - y monophonic path is called an x - y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if every edge of G lies on a detour monophonic path...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Titus,P, Ganesamoorthy,K
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2014
Materias:	edge detour monophonic set edge detour monophonic number minimal edge detour monophonic set upper edge detour mono-phonic set upper edge detour monophonic number.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200004
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172014000200004
record_format	dspace
spelling	oai:scielo:S0716-091720140002000042018-10-30Upper Edge Detour Monophonic Number of a GraphTitus,PGanesamoorthy,K edge detour monophonic set edge detour monophonic number minimal edge detour monophonic set upper edge detour mono-phonic set upper edge detour monophonic number. For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x - y monophonic path is called an x - y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if every edge of G lies on a detour monophonic path joining some pair of vertices in S.The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G).An edge detour monophonic set S ofG is called a minimal edge detour mono-phonic set ifno proper subset ofS is an edge detour monophonic set of G. The upper edge detour monophonic number of G, denoted by edm+(G),is defined as the maximum cardinality of a minimal edge detour monophonic set ofG. We determine bounds for it and characterize graphs which realize these bounds. For any three positive integers b, c and n with 2 ≤ b ≤ n ≤ c, there is a connected graph G with edm(G) = b, edm+(G) = c and a minimal edge detour monophonic set of cardinality n.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.33 n.2 20142014-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200004en10.4067/S0716-09172014000200004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	edge detour monophonic set edge detour monophonic number minimal edge detour monophonic set upper edge detour mono-phonic set upper edge detour monophonic number.
spellingShingle	edge detour monophonic set edge detour monophonic number minimal edge detour monophonic set upper edge detour mono-phonic set upper edge detour monophonic number. Titus,P Ganesamoorthy,K Upper Edge Detour Monophonic Number of a Graph
description	For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x - y monophonic path is called an x - y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if every edge of G lies on a detour monophonic path joining some pair of vertices in S.The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G).An edge detour monophonic set S ofG is called a minimal edge detour mono-phonic set ifno proper subset ofS is an edge detour monophonic set of G. The upper edge detour monophonic number of G, denoted by edm+(G),is defined as the maximum cardinality of a minimal edge detour monophonic set ofG. We determine bounds for it and characterize graphs which realize these bounds. For any three positive integers b, c and n with 2 ≤ b ≤ n ≤ c, there is a connected graph G with edm(G) = b, edm+(G) = c and a minimal edge detour monophonic set of cardinality n.
author	Titus,P Ganesamoorthy,K
author_facet	Titus,P Ganesamoorthy,K
author_sort	Titus,P
title	Upper Edge Detour Monophonic Number of a Graph
title_short	Upper Edge Detour Monophonic Number of a Graph
title_full	Upper Edge Detour Monophonic Number of a Graph
title_fullStr	Upper Edge Detour Monophonic Number of a Graph
title_full_unstemmed	Upper Edge Detour Monophonic Number of a Graph
title_sort	upper edge detour monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2014
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200004
work_keys_str_mv	AT titusp upperedgedetourmonophonicnumberofagraph AT ganesamoorthyk upperedgedetourmonophonicnumberofagraph
_version_	1718439797630959616

Upper Edge Detour Monophonic Number of a Graph

Ejemplares similares